Step 1Heat the oven to 325 degrees.
Step 2In the bowl of a stand mixer using the paddle attachment, or in a large mixing bowl using an electric mixer, beat the butter and 1 cup powdered sugar over medium speed until creamy. Beat in 3 tablespoons lemon zest and the extract.
Step 3In a medium bowl, combine the flour, cornstarch and salt. Beat in the dry ingredients over low speed.
Step 4Shape the dough into a disk, cover with plastic wrap and refrigerate until chilled and firm, about 1 hour.
Step 5Roll the chilled dough to a thickness of three-eighths inch between two sheets of lightly floured wax paper to prevent sticking. Cut the dough into desired shapes using cookie cutters.
Step 6Place the cookies an inch apart on cookie sheets and bake until the edges are slightly golden, about 10 minutes, depending on size. Cool on racks until the cookies are just warm.
Step 7To make the glaze, combine the remaining 1 1/2 cups powdered sugar and remaining 2 teaspoons lemon zest and fresh lemon juice in a medium bowl, whisking until smooth (add additional lemon juice or water to thin or powdered sugar to thicken, if needed).
Step 8To frost, turn the warm cookies over and dip the tops into the glaze. If desired, sprinkle with yellow sugar. Set aside until the glaze is hardened. Store the shortbread in tins with wax paper separating the layers.